where \(\mathbf {\bar{\rho }}_i^*\)  is the phase align point of \(i\) th sub-array which will be determined by maximizing \(\left\lbrace g\left(\Delta \phi _m (\mathbf {\bar{\rho }}_i^*)\right)\right\rbrace _{m\in \mathbb {M}_i}\)  and described at the end of the section. By (REF ), the maximum sin-AoD deviation \(\max _{m\in \mathbb {M}_i}\left|\Delta \phi _{m}(\mathbf {\bar{\rho }}_i^*)\right|\)  of \(\mathbb {M}_i\)  is reduced by \(L\)  times [1]}, which is \(|\mathbb {I}_i|= \frac{\Delta \phi _{\max }}{L}\) . Therefore, to prevent the outlier, \(N_i\)  should satisfy the following:
\(\frac{\Delta \phi _{\max }}{L} \le \frac{\Delta \phi _{\mathrm {HPBW}} (N_i )}{2} \rightarrow N_i \le L \frac{\Delta \phi _{\mathrm {HPBW}}/2}{\Delta \phi _{\max }} N\left(\triangleq kN\right).\) 
